The distance between the function image and two adjacent intersections of a straight line y=2 is equal to π.

∴ Function period T=π=2π/w

∴w=2

∴f(x)=2sin(2x+π/6)

Let -π/2+2kπ≤2x+π/6≤π/2+2kπ.

k∈Z

We get: kπ-π/3≤2x+π/6≤kπ+π/6.

k∈Z

The answer should be C.